

A284391


1limiting word of the morphism 0 > 1, 1 > 001.


4



1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1
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OFFSET

1


COMMENTS

The morphism 0 > 1, 1 > 001 has two limiting words. If the number of iterations is even, the 0word evolves from 0 > 1 > 001 > 11001 > 00100111001; if the number of iterations is odd, the 1word evolves from 0 > 1 > 001 > 11001 > 00100111001 > 110011100100100111001, as in A284391. The 0limiting word results from the 1 limiting word by replacing the initial 00 by 1.
Conjecture: the limiting frequency of 0's in both limiting words is 1/2.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


MATHEMATICA

s = Nest[Flatten[# /. {0 > {1}, 1 > {0, 0, 1}}] &, {0}, 9]; (* A284391 *)
Flatten[Position[s, 0]]; (* A284392 *)
Flatten[Position[s, 1]]; (* A284393 *)


CROSSREFS

A284388 shifted right. Cf. A284392, A284393.
Sequence in context: A267869 A068434 A323511 * A127015 A281114 A286749
Adjacent sequences: A284388 A284389 A284390 * A284392 A284393 A284394


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Mar 30 2017


STATUS

approved



